The derivation in Section REF  allows us to apply
existing convergence theory for the Bregman proximal point method
for monotone inclusions to
the proposed algorithms () and ().
The literature on the Bregman proximal point method
for monotone inclusions [1]}, [2]}, [3]}
focuses on the convergence of iterates,
and this generally requires additional assumptions on
\(\phi _\mathrm {p}\)  and \(\phi _\mathrm {d}\) 
(beyond the assumptions of convexity made in Section REF ).
In this section we present a self-contained convergence analysis
and give a direct proof of an \(O(1/k)\)  rate of ergodic convergence.
We also give a self-contained proof of convergence of the
iterates \(x^{(k)}\)  and \(z^{(k)}\) .
